While spin–orbit torque (SOT) devices are extensively investigated due to their potential for use in neural network computation, it remains challenging to explore the hardware for neural networks. In this paper, the field‐free memristive SOT switching of the CoPt single layer is used to propose a neuromorphic hardware circuit for detecting edges in images. Owing to its threefold symmetry of inversion, the polarity of SOT switching can be reversed by rotating the current by 60°. Moreover, the process of current‐induced SOT switching exhibits stable multi‐state magnetic switching behavior, and can be controllably tuned by using the pulse of the current. As the slope of the applied ramp pulse current increased, the wave of the anomalous Hall resistance changed from a curve with normally memristive property to trigonometric, and finally to cosine. The design of the hardware circuit for a single SOT device is subsequently formulated to detect the edges in images. The results of experiments verified the capability of this device to detect the edge lines in images with high accuracy, which confirms its potential for use in the hardware of neuromorphic computing platforms. The work here provides guidance for the application of SOT‐based devices to neuromorphic hardware.